Signatures of quantumness: identification, quantification and dynamical preservation

The quanti cation of quantumness is necessary to assess how much a physical system departs from a classical behaviour and thus gauge the quantum enhancement in opera- tional tasks such as information processing and computation. For arbitrary multiparti- cle systems, the quanti cation of quantumness typically involves nontrivial optimisation problems, and may require demanding tomographical techniques. We have developed an experimentally feasible approach to the evaluation of geometric measures of quantumness, according to which the distance from the state of the system to a suitable set of classi- cal states is considered. Our approach provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, and gen- uine multiparticle entanglement, as well as to quantum coherence, for any general state. For global and partial entanglement, as well as quantum coherence, useful bounds have been obtained with minimum e ort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N is required. We have demonstrated the power of our approach to estimate and quantify di erent types of multiparticle entanglement in a variety of N-qubit states useful for quan- tum information processing and recently engineered in laboratories with quantum optics and trapped ion setups... [edited by author]